Question

In triangle OPQ right angled at P, OP= 7 cm and OQ-PQ=1 cm. Determine the value of sinQ and cos Q.

Answer 1

The value of the trigonometric ratios are:

sin Q = (7/25)

cos Q = (24/25)

How to use trigonometric ratios?

Let

OQ= x cm then

PQ = 1 + x

OP= 7

by Pythagoras theorem we get

7² + x² = (1 + x)²

49 + x² = x² + 2x + 1

2x = 48

x = 24

Thus:

PQ = 24

OQ = 25

Since we know all 3 sides we can calculate sin Q and cos Q which are:

sin Q = (7/25)

cos Q = (24/25)